F. Becattini
University of Florence
and FIAS Frankfurt
Chemical equilibrium
and chemical freeze-out
OUTLINE
Introduction
Chemical freeze-out in UrQMD
Revisiting the data
Conclusions
Wroclaw, June 14 2013
Three days of...
Chemical Freeze-Out vs QCD critical line
Colliding nuclei at different energies we obtain different chemical
Freeze-out points
Extrapolated T-µ critical line
is flatter than the CFO curve
F.B., J. Manninen and M. Gazdzicki, Phys. Rev. C 73 (2006) 044905
A closer look
F.B., M. Bleicher, T. Kollegger, M. Mitrovski, T. Schuster and R. Stock, Phys. Rev. C 85 (2012)044921
Is the agreement between SHM and data an indication of common
freeze-out?
If yes, we should see a deterioration of fit quality to a simulation including
post-hadronization inelastic rescattering
PROGRAMME
Centrality dependence
Kinetic freeze-out (at RHIC energy)
DOES vary significantly as a
function of centrality, whereas
chemical does not.
Interpretation: if kinetic decoupling
occurs in the expanding hadron gas
stage, it MUST depend on the
geometry, roughly on Surface/Volume
ratio. On the other hand, chemical
seems NOT to depend, which is an
indication of it being very close to the
critical line
U. Heinz, G. Kestin, CPOD 2006
nucl-th: 0612105
Main effect of hadronic rescattering (afterburner): antibaryon loss
Second step: fitting to SHM (γS) -
Hydro only
using exp. errors
Major effects of including afterburning:
Lowering the output c.f.o. T by ~ 10 MeV
●
Sizeable worsening of fit quality
●
Third step: fitting to SHM (γS) removing antibaryons
Hydro+UrQMD
Hydro
Major effects of excluding antibaryons:
●
●
Essential recovery of “original” freeze-out point
Much better fit quality
What does the data say?
SPS energy
A recently published p yield by NA49 in Pb-Pb at 17.2 GeV turned out to be consistently
lower than the predicted by SHM.
Predicted: 6.86
(F.B., J. Manninen and M. Gazdzicki,
Phys. Rev. C 73 (2006) 044905)
Measured: 4.23±0.35
New fit to Pb-Pb mult's at 17.2 GeV
Lower T, lower quality
F. B., M. Bleicher, T. Kollegger, M. Mitrovski, T. Schuster and R. Stock Phys. Rev. C 85 (2012) 044921
Possible explanation: the effect of post­hadronization rescattering
Effect of UrQMD
afterburning on initial
statistical hadronic yields
from a hydro code
See also S. Bass and A. Dumitru, Phys. Rev. C 61 (2000) 064909
Residual distribution
of a fit to hadronic yields
excluding anti­baryons:
Similar pattern of deviations
LHC energy
The p ( p)/π yield in PbPb at 2.76 TeV is lower than predicted by the
statistical hadronization model by 40% (prediction by A. Andronic et al., J.Phys. G38 (2011) 124081)
Advocated as an effect of post-hadronization rescattering:
J. Steinheimer, J. Aichelin and M. Bleicher, Phys. Rev. Lett. 110 (2013) 042501
Y. Pan and S. Pratt, Baryon Annihilation in Heavy Ion Collisions arXiv:1210.1577 [nucl­th]
F. B., M. Bleicher, T. Kollegger, T. Schuster, J. Steinheimer and R. Stock, Hadron Formation in Relativistic Nuclear Collisions and the QCD Phase Diagram,'' arXiv:1212.2431
[nucl­th].
Physical picture Where did we start from?
F.B., An introduction to the Statistical Hadronization
Model, arXiv:0901.3643
How to reconstruct hadronization conditions?
Strictly speaking, the latest hadro chemical equilibrium point (LHCEP)
Estimating the effect of the afterburning
with an analytical calculation (e.g. Pratt) or
a Monte-Carlo (UrQMD)
Critical line = Hadronization
Latest chemical equilibrium
point
Chemical freeze-out
Kinetic freeze-out
“Corrected” fit to ALICE data
Higher T, much better quality
Comparing reconstructed LCHP's with lattice QCD
Lattice calculations from
F. Karsch, J. Phys. G 38, 124098 (2011); S. Borsanyi et al., ibidem 124101
G. Endrodi, Z. Fodor, S. D. Katz and K. K. Szabo, JHEP 1104, 001 (2011)
See also: The critical line of two­flavor QCD at finite isospin or baryon densities from imaginary chemical potentials. P. Cea, L. Cosmai, M. D'Elia, A. Papa, F. Sanfilippo, Phys.Rev. D85 (2012) 094512 We now start to see the details...
Conclusions and outlook
It has been believed that
Chemical freeze-out = chemical equilibrium ≃ hadronization ≠
QCD critical line at higher µB
In fact, there is strong evidence that:
Chemical freeze-out ≠ chemical equilibrium ≅ hadronization = critical line
There should be some (slight) dependence of C.F.O. on centrality:
we are going to repeat the analysis with data taken in different
centrality bins.
A special thank to Reinhard Stock
S. Das, talk at Quark Matter 2012
Core-corona model
γS =1 for the core
γS < 1 in heavy ion collisions is the effect of peripheral single NN
collisions, for which γS ~ 0.5
Calculates Nc from Glauber
This approach reproduces very well the centrality dependence of strangeness
enhancement (F.B., J. Manninen QM 2008 and J. Aichelin, K. Werner)
QCD phase transition
At µB = 0 the transition is continuous (crossover)
Tc ~ 160 MeV
Relativistic heavy ion collisions
How to produce “matter”
with ε >>1 GeV/fm3
lasting for τ > 1 fm/c
in a volume much larger than a hadron?
Accelerator
Lab
√sNN
Nuclei
SPS (90's)
CERN
6-18
Pb-Pb
RHIC (00-..
RHIC
7.7-200
Au-Au
LHC (09-..)
CERN
2750
Pb-Pb
Sketch of the nuclear collision process
τeq
Pre-equil.
phase
Hadron radiation and freeze­out Hadron radiation provides direct information about the thermodynamical state of the system at the
stage when hadrons cease interactions and decouple
FREEZE­OUT:
Chemical = when inelastic interactions cease
Kinetic = when also elastic interactions cease
QGP Critical line = Hadronization Chemical freeze­out Kinetic freeze­out
Does the system stay in chemical equilibrium up to chemical freeze­out?
For many years the answer has been YES
F. B., J. Manninen, Phys. Rev. C 78 (2008) 054901